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Title: An algebraic method for constructing stable and consistent autoregressive filters

In this paper, we introduce an algebraic method to construct stable and consistent univariate autoregressive (AR) models of low order for filtering and predicting nonlinear turbulent signals with memory depth. By stable, we refer to the classical stability condition for the AR model. By consistent, we refer to the classical consistency constraints of Adams–Bashforth methods of order-two. One attractive feature of this algebraic method is that the model parameters can be obtained without directly knowing any training data set as opposed to many standard, regression-based parameterization methods. It takes only long-time average statistics as inputs. The proposed method provides a discretization time step interval which guarantees the existence of stable and consistent AR model and simultaneously produces the parameters for the AR models. In our numerical examples with two chaotic time series with different characteristics of decaying time scales, we find that the proposed AR models produce significantly more accurate short-term predictive skill and comparable filtering skill relative to the linear regression-based AR models. These encouraging results are robust across wide ranges of discretization times, observation times, and observation noise variances. Finally, we also find that the proposed model produces an improved short-time prediction relative to the linear regression-based AR-modelsmore » in forecasting a data set that characterizes the variability of the Madden–Julian Oscillation, a dominant tropical atmospheric wave pattern.« less
Authors:
 [1] ;  [2] ;  [3] ;  [3]
  1. Department of Mathematics, the Pennsylvania State University, University Park, PA 16802 (United States)
  2. (United States)
  3. Department of Mathematics, North Carolina State University, Raleigh, NC 27695 (United States)
Publication Date:
OSTI Identifier:
22382189
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 283; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; CHAOS THEORY; COMPARATIVE EVALUATIONS; ERRORS; FILTERS; LIMITING VALUES; MATHEMATICAL MODELS; NOISE; NONLINEAR PROBLEMS; OSCILLATIONS; STABILITY; STATISTICS